Smith was scintillating for the Coyotes, especially from the second period on. He did everything possible to keep the Coyotes afloat and give his team a chance to win it.

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And when Oliver Ekman-Larsson beat Jaroslav Halak with a slap shot from the blue line, it sealed the Coyotes' 3-2 overtime victory over the St. Louis Blues.

(St. Louis Blues/Mark Buckner)

Patrik Berglund (21) and the Blues had a hard time solving

Phoenix goalie Mike Smith (41) Tuesday night.﻿

Ekman-Larsson's goal 56 seconds into overtime came on Phoenix's 19th shot of the game and helped the Coyotes pick up their seventh win in eight games.

The Blues (11-2-3) peppered Smith with shot after shot, as Smith was able to keep 37 of the 39 shots he saw out of the net. Smith, who picked up his 11th win of the season, bent but didn't break.

"The old rope a dope," Smith said jokingly. "Obviously we’re happy with the two points. They can’t take those back from us now.

"That’s definitely not the way we want to be as a team this year. When you play really good hockey teams, I think we've got to raise our level."

Ekman-Larsson was one of them, who was able to take in Mike Ribeiro's pass and fire a shot that Halak was screened on.

"It was a great play there by Ribeiro," said Ekman-Larsson, who has four goals and three of them game-winners. "I saw [Shane] Doan was coming in from the corner so I shot it, and it was perfect."

Blues defenseman Alex Pietrangelo was on the ice and may have partially screened Halak, who stopped 16 shots, on the play.

"It's obviously a good shot coming down the middle there," Pietrangelo said. "Someone's got to block it. I didn't see what happened up top. I was trying to block the shot. I think I kind of got in the way of Jaro, too, there. Mostly the onus is on us there. Jaro really had no chance. I don't think he saw it.

"Where he is and how it happened, the exchange, I have to look at it again. You don't want to screen your goalie and not give him the opportunity to see it."

Mikkel Boedker and David Moss also scored for the Coyotes (13-4-2), and Ribeiro had two assists.

Maxim Lapierre and Roman Polak scored for the Blues, who saw their three-game winning streak snapped.

Blues coach Ken Hitchcock went back to a common theme, something he felt cost the Blues in their playoff series loss to the Los Angeles Kings last spring.

"The same thing happened [against] Pittsburgh," Hitchcock said, referring to the 2-1 victory Saturday. "We won the game, but if we want to get to the next level, we've got to find a solution to outwork the goalie. We did a lot of good things in the second and third period, but we've got to outwork the goalie. It doesn't matter how you get it done. You've just got to get it done. If we want to go to the top echelon and be there and be part of that, that's one of the things we want to see get done."

Polak scored his second of the season when he pinched in from the right point, took a terrific pass from Alexander Steen and beat Smith over the glove on the short side 2:49 into the third period to tie the game 2-2.

The assist extended Steen's career-best and NHL-leading point streak to 11 games. Steen has 10 goals and 14 points during the run.

With the game tied 2-2, Smith made the save of the game, robbing Derek Roy with a glove save with 7:05 remaining in the game after Roy came into the zone with a slick spin move.

Moments later, Smith was up to the task again on Vladimir Tarasenko with a left-pad save and Brenden Morrow barreling down on him.

Smith robbed Roy again 21 seconds into overtime, this time grabbing Roy's backhand in front on a high-percentage scoring chance.

"That was a great move; the puck was kind of bouncing and he was able to get it between his legs," Smih said of Roy. "It was more luck than anything. I think it just ended up in my glove. But I’ll take it."

Patrik Berglund also whiffed on an open chance in the third period off a T.J. Oshie feed.

"It's the whole focus of finishing, burying it in the back of the net, not relaxing," Hitchcock said. "Some guys are struggling offensively right now ... we've got to get them going, but that's pretty much it. We had opportunities, we created a number of offensive opportunities off our work. We really started to skate the second and third period, really gave them trouble and did a great job of keeping the puck away from Smith in the second period, but at the end of the day, you've just got to put it in the net.

"We worked, we competed and we created scoring chances. We had some people that were really effective as the game wore on, became major players in the game for us, but we didn't outwork the goalie."

Smith made two saves in overtime before seeing Ekman-Larsson's winner.

"I don’t love it," Smith said, who's seen 555 shots this season to lead the NHL. "It’s just the way things have worked out so far. Obviously, we want to tighten that up and get those shot totals down. But right now, we’re finding ways to win games. Right now, we’re just happy to get the two points."

Blues captain David Backes credited Smith with a fine game but also felt he and his teammates need to finish.

"He made some phenomenal saves," Backes said. "That being said, we've got good players on our team that need to find a shot to get by him, myself especially and maybe we're having a different conversation now."

Lapierre put the Blues ahead with his third point in as many games and second goal in three games when he redirected Jay Bouwmeester's wrist shot past Smith 5:53 into the game for a 1-0 lead.

It was the eighth straight game in which the Blues scored the first goal of the game and 13th time in 16 games overall.

But Phoenix closed out the first period with two goals off a pair of St. Louis mistakes.

Moss tied the game when he converted a T.J. Oshie turnover in the defensive zone, snapping a shot from the right circle past Halak at 7:49 of the first period. It was Moss' first goal since he scored against the Edmonton Oilers on April 10, a 26-game span.

Boedker scored his fourth of the season -- all on the road -- after the Blues missed out on a pinch, as Kevin Shattenkirk failed to keep a puck in the offensive zone and the Coyotes came away with a 3-on-1. Boedker took a feed into the slot from Rob Klinkhammer and one-timed a slap shot past Halak with 31 seconds left in the first for a 2-1 Phoenix lead.

"We played a game today that started off pretty slow," Backes said. "I think we liked the way we progressed throughout the game but dug a little hole. We had to give everything we had just to get back tied. You double up a team in shots, you expect to bury a few more and that's upon us to find a way to do that."

That was the risk of starting slow for the Blues after an emotional win over the Penguins Saturday.

"That's the risk you run sometimes when you have an emotional game like that," Bouwmeester said. "The next game you come out flat. We talked about it and tried not to let it happen but it did. That's something we can take from that game, need a better start.

"We had a lot of time in their end, had some chances (in the third period). But you know, that's kind of the next step you have to take. You have to make good on those ... and we didn't."